Having an index on 3 integer columns (column1, column2, column3), the analyse command generates the stat1 and stat3 tables. I see the following statistics for this index in the sqlite_stat1 table:

"4600132 1289 1275 1"

When I execute the following SQL query, this index is not used but the query optimizer prefers to use the primary index which is on the column3, which is about 60 times slower than using the index. ( 20000 ms vs 300 ms)